The invention is an off shoot of known technology for making paper tubes from ribbons of flat feed stocks. A basic apparatus for making such paper tubes is disclosed in U.S. Pat. No. 3,538,817, issued Nov. 10, 1970 to Erik Brown, the disclosure of which is hereby incorporated herein by reference. Additionally, FIG. 1 of this application is based on FIG. 1 of that patent. It shows apparatus in which flat paper feedstocks 13, 14, 15, 16 are wrapped around a mandrel 11 rotatably supported in (but not rotatably driven by) a support 12. The tube 43 formed from the feedstocks 13, 14, 15, 16 is advanced relative to the mandrel 11 by the action of an upstream drive belt 34 and a downstream drive belt 40, each of which is wrapped around (and is in surface engagement with) the tube 43. The completed tube 43 (i.e., the tube downstream of the downstream drive belt 40) is cut into lengths by a saw 44.